We were given this today in class and told to complete it. I am still confused by it.

" A company produces and sells three interrelated products w, x, and y. They need to determine the optimum weekly production of each, ie w units of W, x units of X, y units of Y. However, the price demand function for the each of the products are linked together as follows:

(b) note you only have one cost function for all three products together, so you cannot find separate profit functions for each product. therefore, add all revenues from (a) and deduct the total cost function.

(c) since you have only one profit function with three variables, you find three partial derivatives of that profit function (on w, x and y).

(d) did you study this in calculus? to maximise function, you find the critical point (where it's first derivative=0) and check if this point is mix, max or something else. here you have one function with three variables, so you deal with points where their partial derivatives =0.

Mar 3rd 2011, 04:41 AM

iCONFUSED

Quote:

Originally Posted by Volga

(a) correct

(b) note you only have one cost function for all three products together, so you cannot find separate profit functions for each product. therefore, add all revenues from (a) and deduct the total cost function.

(c) since you have only one profit function with three variables, you find three partial derivatives of that profit function (on w, x and y).

(d) did you study this in calculus? to maximise function, you find the critical point (where it's first derivative=0) and check if this point is mix, max or something else. here you have one function with three variables, so you deal with points where their partial derivatives =0.

- open the brackets and simplify to get the final profit function. Then move to (c)

(c) Find partial derivatives of the above function w.r.t. w, x and y.

Example: if y=30a+40b+50c, then partial derivative of y with respect to a is 30 - treat other two variables as constants, and derivative of a constant is zero. I don't want to do your homework for you, so I gave a separate example.